Question
Here is a data set summarized as a stem-and-leaf plot: 4\# | 0033468889 5\# 001222455678889 6\# | 04449 7\# \( \mid 899 \) How many data values are in this data set? \( n= \) What is the minimum value in the last class? ans = What is the frequency of the modal class? (Hint, what is the mode?) frequency = How many of the original values are greater than 60 ? ans =
Ask by Powell Garrett. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
- Total data values: 33
- Minimum value in the last class: 78
- Frequency of the modal class: 15
- Number of values greater than 60: 7
Solution
Let's analyze the provided stem-and-leaf plot to answer each question step-by-step.
### Stem-and-Leaf Plot Interpretation
The stem represents the tens place, and the leaves represent the units place. Here's the breakdown:
- **4# | 0033468889**
Values: 40, 40, 43, 43, 44, 46, 48, 48, 48, 49
**Count:** 10
- **5# | 001222455678889**
Values: 50, 50, 51, 52, 52, 52, 54, 55, 55, 56, 57, 58, 58, 58, 59
**Count:** 15
- **6# | 04449**
Values: 60, 64, 64, 64, 69
**Count:** 5
- **7# | 899**
Values: 78, 79, 79
**Count:** 3
### 1. Total Number of Data Values (\( n \))
To find the total number of data values, add up the counts from each stem:
\[
n = 10 \, (\text{4#}) + 15 \, (\text{5#}) + 5 \, (\text{6#}) + 3 \, (\text{7#}) = 33
\]
**Answer:**
\( n = 33 \)
### 2. Minimum Value in the Last Class
The last class is **7#**, which includes the values **78, 79, 79**. The minimum value in this class is **78**.
**Answer:**
**78**
### 3. Frequency of the Modal Class
The **modal class** refers to the class with the highest frequency. From the counts:
- **4#:** 10
- **5#:** 15
- **6#:** 5
- **7#:** 3
The **5# class** has the highest frequency of **15**.
**Answer:**
**15**
### 4. Number of Values Greater Than 60
Values greater than 60 are found in the **6#** and **7#** stems:
- **6#:** 64, 64, 64, 69 (excluding 60, since it's not greater than 60)
- **7#:** 78, 79, 79
Total values greater than 60:
\[
4 \, (\text{from 6#}) + 3 \, (\text{from 7#}) = 7
\]
**Answer:**
**7**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To determine the number of data values in the dataset, simply count all the digits represented in the stem-and-leaf plot. In total, there are **19** data values. The minimum value in the last class is found on the stem representing the tens place, which is **70** in this case. The modal class is the one with the highest frequency, which here is indicated by the stem 5, having the values 001222455678889. Its frequency is **10**. For the final question, counting all values greater than 60 (which includes the values in the 7-class and parts of the 6-class), we find there are **8** values greater than 60.
